Apparatus and method for reducing phase noise in oscillator circuits

ABSTRACT

A resonant oscillator circuit includes an active device and a resonator that causes the active device to oscillate at a resonant frequency of the resonator. The active device includes one or more transistors that are DC biased using one or more resistors. The bias resistors generate thermal noise that is proportional to the resistance value. An external inductor circuit is connected across the output terminals of the active device and in parallel with the resonator. The external inductor circuit shorts-out at least some of the thermal noise that is generated by the bias resistors, and thereby reduces the overall phase noise of the resonant oscillator.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. ProvisionalApplication No. 60/258,492, filed on Dec. 29, 2000, which isincorporated herein by reference in its entirety.

BACKGROUND OF THE INVENTION

[0002] Field of the Invention

[0003] The present invention generally relates to phase noise reductionin oscillator circuits, and more specifically to phase noise reductionin differential crystal oscillator circuits.

[0004] Background Art

[0005] Radio frequency (RF) transmitters and receivers perform frequencytranslation by mixing an input signal with a local oscillator (LO)signal.

[0006] Preferably, the LO signal should have a frequency spectrum thatis as close to a pure tone as possible in order to maximize systemperformance during the signal mixing operation. The deviation of the LOsignal from a pure tone is quantified as phase noise or phase jitter,and is generally referred to as spectral purity. In other words, a LOsignal with good spectral purity has low phase noise.

[0007] Typically, the LO signal is generated from a lower frequencyreference signal in order to maximize spectral purity. The lowerfrequency reference signal is often frequency multiplied to generate thehigher frequency LO signal. For instance, a phase lock loop (PLL)generates an output signal that is a frequency multiple of an inputreference signal, but is phase-locked to the input reference signal. Insome applications, several multiplication stages are required to achievethe desired LO frequency.

[0008] Frequency multiplication can negatively impact spectral purity byincreasing phase noise in the output LO signal. Phase noise increasesbecause frequency multiplication (which is equivalently phasemultiplication) enhances phase noise spectral density as the square ofthe multiplication factor. Therefore, the higher order multiplication ofa noisy reference signal is to be avoided.

[0009] A crystal oscillator is often used to generate the referencesignal because of its inherently low phase noise attributes. A crystaloscillator includes an active device and a crystal, where the impedanceof the crystal is a short (or an open) circuit at a natural resonantfrequency. By connecting the crystal in parallel with the active device,a positive feedback path is created between the oscillator terminals atthe crystal resonant frequency. The positive feedback causes the activedevice to oscillate at the crystal resonant frequency.

[0010] A crystal resonator has a relatively high quality factor, or “Q”,when compared to other types of resonators. Therefore, the bandwidth ofthe crystal resonance is relatively narrow so that the impedance changeof the crystal in the vicinity of its resonant frequency is relativelyabrupt. The relatively high Q of the crystal improves the spectralpurity of a crystal oscillator output signal because the crystalresonance determines the frequency of oscillation for the active devicein the oscillator. Accordingly, a crystal oscillator has a relativelylow phase noise compared to other resonant oscillator configurations.

[0011] The active device in the crystal oscillator typically includesone or more transistors that can be configured in various arrangements.Transistors necessarily require some type of bias circuitry to power thetransistors. The bias circuitry typically includes one or moreresistors, which inherently produce thermal noise that is proportionalto the total resistance. The thermal noise voltage modulates the zerocrossings of the oscillation waveform, and increases the phase noisefloor around the oscillation frequency. The increased phase noise floordetracts from the inherently low phase noise of a crystal oscillator.Additionally, as stated above, a high phase noise floor is undesirablein reference signals that drive frequency synthesizers because theoutput phase noise increases with square of any frequency multiplicationthat is performed by the synthesizer.

[0012] Therefore, what is needed is an oscillator circuit architecturethat nullifies the thermal noise voltage that is created by the biasresistors that power the active device in the oscillator circuit.

BRIEF SUMMARY OF THE INVENTION

[0013] The present invention is directed to an external inductor circuitthat reduces phase noise in a resonant oscillator circuit. The externalinductor circuit provides a DC path across the oscillator outputterminals and shorts-out thermal noise that is generated by theoscillator circuit, thereby preventing the thermal noise from increasingthe phase noise floor of the oscillator output signal.

[0014] A resonant oscillator circuit includes an active device and aresonator, such as a crystal resonator. The resonator causes the activedevice to oscillate at the resonant frequency f₀ of the resonator bycreating positive feedback (or negative resistance) in the active deviceat the resonant frequency f₀.

[0015] The active device includes one more transistors that require DCbias circuitry to provide power for the transistors. The DC biascircuitry typically includes one or more resistors that generate thermalnoise that increases in proportion to the total resistance. The externalinductor circuit is connected across the terminals of the oscillatorcircuit, and in parallel with the resonator. The external inductorcircuit shorts-out the thermal noise from the resistors so the thermalnoise does not increase the phase noise floor of the oscillator outputsignal.

[0016] The external inductor circuit includes an inductor and a resistorconnected in series, which provide the DC path that shorts-out thethermal noise from the bias resistors. The value of the inductor issufficiently large so as not to interfere with the positive feedbackpath that is created by the resonator at the resonant frequency f₀. Inother words, the parallel combination of the inductor and the resonatorshould not substantially shift the resonant frequency f₀ of theresonator, so as not to change the operating frequency of theoscillator. This can be accomplished by assuring that any parasiticresonance caused by the external inductor is sufficiently lower infrequency than the intended resonant frequency of the resonator.

[0017] The value of the resistor is sufficiently large to suppress anyunwanted parasitic oscillations that are caused by the external inductorresonating with the resonator capacitance. However, the resistor in theexternal inductor circuit should be no larger than necessary as it willgenerate its own thermal noise that is proportional to the resistorvalue just like the bias resistors for the active device.

[0018] In embodiments, the resistor value is no larger than the biasresistors associated with the active device.

[0019] Further features and advantages of the present invention, as wellas the structure and operation of various embodiments of the presentinvention, are described in detail below with reference to theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS/FIGURES

[0020] The present invention is described with reference to theaccompanying drawings. In the drawings, like reference numbers indicateidentical or functionally similar elements. Additionally, the left-mostdigit(s) of a reference number identifies the drawing in which thereference number first appears.

[0021]FIG. 1A illustrates an oscillator configuration;

[0022]FIG. 1B illustrates an ideal oscillator output signal that doesnot include phase noise;

[0023]FIG. 1C illustrates an oscillator output signal that does includephase noise;

[0024]FIG. 2A illustrates a series resonant circuit;

[0025]FIG. 2B illustrates a parallel resonant circuit;

[0026]FIG. 2C illustrates a crystal resonator;

[0027]FIG. 2D illustrates an equivalent circuit for a crystal resonator;

[0028]FIG. 2E illustrates a crystal resonator having an additionalcapacitance in parallel with the crystal resonator;

[0029]FIG. 2F illustrates an equivalent circuit for the crystalresonator having the additional capacitance;

[0030]FIG. 3A illustrates an impedance plot for a series resonantdevice;

[0031]FIG. 3B illustrates an impedance plot for a parallel resonancedevice;

[0032]FIG. 3C illustrates an impedance plot for a crystal resonatorhaving a series resonance and a parallel resonance;

[0033]FIG. 4 illustrates various resonant circuit impedance plots fordifferent Q values;

[0034]FIG. 5 illustrates a synthesizer that is driven by a oscillator;

[0035]FIG. 6 illustrates an oscillator 600 that has an external inductorcircuit to short-out thermal noise that is generated by the oscillatorbias resistors according to embodiments of the invention;

[0036]FIG. 7 illustrates a flowchart 700 that further describes theoperation of the oscillator 600;

[0037]FIG. 8 illustrates a differential crystal oscillator 800 accordingto embodiments of the present invention;

[0038]FIG. 9 illustrates the differential crystal oscillator 800 with anexternal inductor circuit to short-out thermal noise that is generatedby the oscillator bias resistors according to embodiments of the presentinvention; and

[0039]FIG. 10 illustrates an alternate embodiment for the externalinductor circuit according to embodiments of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

[0040] 1. Oscillator Configuration

[0041]FIG. 1A illustrates an oscillator circuit 100 having a resonator102, an active device 104, and at least one resistor 106 to bias theactive device 104. The oscillator 100 generates the output signal 112that is preferably a pure tone in the frequency domain at the resonantfrequency f₀ of the resonator 102, as shown in FIG 1B.

[0042] Realistically, the output signal 112 is not a pure tone becauseof the phase noise that is associated with the oscillator circuit 100.As shown in FIG. 1C, the phase noise manifests itself as energy “skirts”114 around the oscillation frequency f₀. To quantify phase noise, thenoise power in a unit frequency bandwidth 116 is determined at an offset118 from the resonant frequency f₀. The measured noise power inbandwidth 116 is then divided by the average total power in the outputsignal 112 to calculate a value for the phase noise.

[0043] The active device 104 is capable of oscillating when there ispositive feedback (or a negative resistance) between an input terminal108 and an output terminal 110. For instance, the active device 104 caninclude one or more transistors that have sufficient gain at thefrequency of interest to oscillate. Exemplary transistors include afield effect transistor (FET) and a bipolar junction transistor (BJT).In embodiments, the active device 104 is configured to include across-coupled differential pair of transistors, which is describedfurther herein.

[0044] The resonator 102 is connected across the terminal 108 and theterminal 110 of the active device 104, and has an impedance thatapproaches a short circuit or an open circuit at the resonant frequencyf₀. For example and without limitation, the resonator 102 can be aseries LC circuit 201 (FIG. 2A), a parallel LC circuit 207 (FIG. 2B), ora crystal 214 (FIG. 2C), all of which are described in further detailbelow. At the resonant frequency f₀, the resonator 102 causes thepositive feedback that is required for the active device 104 tooscillate and produce the output signal 112.

[0045] The series LC circuit 201 has an inductor 202, a capacitor 204,and a parasitic resistor 206 that are connected in series. The impedanceof the LC circuit 201 is depicted in FIG. 3A. As shown in FIG. 3A, theimpedance of the LC circuit 201 approaches 0 ohms at the resonantfrequency f₀, as this is the frequency where the impedance of theinductor 202 and the capacitor 204 cancel each other. The resonantfrequency f₀ is determined according to the following equation:

f ₀=(½π)·1/sqrt(LC)  Eq. 1

[0046] Ideally, the resistance of the parasitic resistor 206 is 0 ohms,in which case the impedance of the LC circuit 201 would be 0 ohms at theresonant frequency f₀. Practically, the resistance of the parasiticresistor 206 is non-zero, and therefore the resistance of the LC circuit201 at f₀ is not 0 ohms. The quality factor (or “Q”) quantifiesbandwidth (or “sharpness”) of the resonance based on the ratio of thecircuit reactance and the parasitic resistance according the equation:

Q=(2πf ₀ L)/R  Eq. 2

[0047] As shown by Eq. 2, Q increases for the series LC circuit 201 asthe resistance R decreases. Correspondingly, the oscillator Q andspectral purity also increases as the resistance R decreases.

[0048] Referring to FIG. 2B, the parallel LC circuit 207 has a capacitor208, an inductor 210, and a resistor 212 that are connected in parallel.The impedance of the LC circuit 207 is depicted in FIG. 3B. As shown inFIG. 3B, the impedance of the LC circuit 207 approaches an open circuitat the resonant frequency f₀, as this is the frequency where theadmittance of the inductor 210 and the capacitor 208 cancel each otherout. Ideally, the parasitic resistor 212 is infinite (i.e. an opencircuit), in which case the impedance of the LC circuit 207 would be anideal open circuit at the resonant frequency f₀. Practically, theparasitic resistor 212 is a not infinite, and therefore the impedance ofthe LC circuit 207 at f₀ is not infinite. Q for a parallel LC circuit isdetermined according to the following equation:

Q=2πf ₀ RC  Eq. 3

[0049] As shown by Eq. 3, Q increases for the parallel LC circuit 201 asthe resistance R increases, Correspondingly, the oscillator Q andspectral purity also increases as the resistance R increases.

[0050] The crystal 214 has a reciprocal relationship (called thepiezoelectric effect) between the mechanical deformation along onecrystal axis and the appearance of an electrical potential along asecond crystal axis. Therefore, deforming a crystal will separatecharges and produce a voltage at the crystal terminals. Conversely, anapplied voltage across the crystal will deform the crystal.

[0051] If the applied voltage is sinusoidal with a variable frequency,then the crystal will go into mechanical oscillation, and exhibit anumber of resonant frequencies.

[0052] The crystal 214 has an equivalent electrical circuit 216 that isshown in FIG. 2D. LC circuit 216 includes a series resonant circuit 217that represents the equivalent circuit corresponding to thepiezoelectric effect for the crystal 214 that was described above. Theseries resonant circuit 217 includes a motional inductor L_(M) 219, amotional capacitor C_(M) 220, and a motional resistor R_(M) 222.Additionally, the LC circuit 216 has a package capacitance C_(P) 218that represents the capacitance associated with the electrical packagethat the crystal is mounted in.

[0053] The impedance plot for the crystal equivalent circuit 216 isshown in FIG. 3C. As shown in FIG. 3C, the impedance plot includes afirst resonance 302 and a second resonance 304. The first resonance 302is a series resonance that occurs at the frequency where the impedanceof the L_(M) 219 and the C_(M) 220 cancel each other, and can becalculated by using Eq. 1. The second resonance 304 is a parallelresonance that occurs at the frequency where the admittance of theseries resonant circuit 217 and the admittance of the C_(P) 218 canceleach other, which can be determined by using Eq. 5 herein.

[0054] In radio frequency applications, 10 MHZ is a popular referencefrequency.

[0055] However, standard value commercially available crystals are notresonant at 10 MHZ without adding an additional capacitance 224 inparallel with the crystal 214 as shown in FIG. 2E. FIG. 2F illustratesthe equivalent circuit 225 of the crystal resonator 214 with the addedcapacitance 224. The additional capacitance 224 can be varied to tunethe parallel resonance 304 to a desired frequency (e.g. 10 MHZ) bychanging the total parallel capacitance of the equivalent circuit 225.

[0056] The Q of a crystal is typically substantially higher thanresonators that are comprised of discrete circuit elements (i.e.discrete inductors and capacitors). For example, FIG. 4 illustratesseveral impedance curves 402 for resonant LC circuits having different Qvalues. Referring to FIG. 4, the curves 402 a-c are representative of LCcircuits that are made of discrete components, such as LC circuits 201and 207 described herein. Whereas, the curve 402 d is representative ofa crystal, such as crystal 214. As shown, the crystal impedance curve402 d has a substantially sharper resonance at the resonant frequency(1.0 MHZ in this example) when compared to the other impedance curves402 a-c. This occurs because the ratio of the motional resistance (R_(M)222) to the motional reactance (L_(M) 219 and C_(M) 220) of the crystal214 is much smaller than the ratio of the parasitic resistance to thereactance of the lumped LC circuits 201 and 207.

[0057] As mentioned above, the bias resistor 106 represents one or moreresistors that bias the active device 104. The active device 104typically includes one or more transistors and incorporates the biasresistor 106 to provide DC power for the transistors. The bias resistor106 can be integrated within active device 104 depending on the specificcircuit configuration that is utilized, as will be understood by thoseskilled in the relevant arts. The bias resistor 106 generates thermalnoise voltage that increases with increasing temperature, resistance,and circuit bandwidth according to the following equation:

V _(n) ²=4kTRB, where:  Eq. 4

[0058] T=temperature in kelvin

[0059] R=resistance

[0060] k=Boltzmann's constant

[0061] B=bandwidth in hertz.

[0062] The thermal noise from the resistor 106 modulates the zerocrossing of the output signal 112 of the oscillator 100. Since theoutput signal 112 is hard limited in the oscillator 100 (because to theoscillator 100 is in saturation), the thermal noise from the resistor106 leads to higher phase noise in the output signal 112. As shown inFIG. 1C, the phase noise manifests itself as energy “skirts” 114 in theoutput signal 112 around the resonant frequency f₀.

[0063] Phase noise is undesirable in reference signals that are thebasis for frequency multiplication. For instance, FIG. 5 illustrates theoscillator 100 driving a synthesizer 502 to generate a LO signal 506.The synthesizer 502 includes a multiplier 504 that multiplies thefrequency of the oscillator output signal 112 by a factor of N, togenerate the LO signal 506 that is used for frequency mixing in a mixer508. Frequency multiplication (which is equivalently phasemultiplication) enhances phase noise spectral density as the square ofthe multiplication factor, so that higher order multiplication of anoisy reference signal should be avoided. More specifically, phase noisedensity in the LO signal 506 will increase as a factor of N², where Nrepresents the amount of frequency multiplication. The mixer 508down-converts a RF signal 510 by frequency mixing the RF signal 510 withthe LO signal 506 to generate an IF signal 512. 2. Phase Noise Reductionin Oscillator Circuits

[0064]FIG. 6 illustrates an oscillator 600 according to embodiments ofthe present invention. The oscillator 600 is similar to the oscillator100 except that the oscillator 600 includes a feedback circuit 602 thatis connected across the active device 104. The feedback circuit 602 isconnected in parallel with the resonator 102 across the terminals 108and 110 of the active device 104. The feedback circuit 602 includesinductor 604 and a resistor 606.

[0065] The feedback circuit 602 provides a DC path from the terminal 108to the terminal 110 for any thermal noise that is generated by the biasresistor 106. As such, the thermal noise from the bias resistor 106 isshorted-out and does not increase the phase noise floor of the outputsignal 112. The feedback circuit 602 is redundant if the resonator 102is the parallel LC configuration 207 (FIG. 2B) because the inductor 210already provides a DC path across the terminals 108 and 110. However,the feedback circuit 602 is not redundant if the resonator 102 is theseries LC configuration 201 (FIG. 2A) because the capacitor 204 operatesas a DC block that prevents DC and low frequency energy from passingthrough the resonator 201. Additionally, the feedback circuit 602 in notredundant for the crystal 214 because the C_(P) 218 and the C_(M) 220(shown in the equivalent circuit 216) also operate as a DC block thatblocks the feedback of DC and low frequency energy.

[0066] In addition to nullifying thermal noise, the inductor 604 in theinductor circuit 602 combines with the parallel capacitance in theresonator 102 to cause an (unwanted) low frequency parasitic resonance.For instance, in the crystal 214, the inductor 604 combines with C_(P)218 (or the parallel combination of C_(P) 218 and C_(ADC) 224) to causean (unwanted) low frequency parasitic resonance. Preferably, the valueof the inductor 604 is sufficiently large so this parasitic resonancedoes not shift the oscillation frequency of the oscillator 600 from theresonant frequency f₀ of the resonator 102. The inductor 604 should beselected so as not interfere with the feedback path provided by theresonator 102 at the resonant frequency f₀. Accordingly, the parallelcombination of the inductor 604 and the resonator 102 should notsubstantially shift the resonant frequency f₀ of the resonator 102, soas not to change the operating frequency of the oscillator 600. This canbe accomplished by assuring that the parasitic resonance that is causedby the inductor 604 is lower than the frequency of the desired resonanceof the resonator 102 by approximately a factor of {square root}{squareroot over (10)}. In other words, the parasitic resonance occurs at afrequency that is approximately {square root}{square root over (10)} ofthe frequency of the desired resonance, or lower. For example andwithout limitation, assuming that the resonator 102 has an intendedresonance at 10 MHZ, then the parasitic resonance caused by the inductor604 should preferably be approximately 3 MHZ, or less. For a givencapacitance value, a minimum value for the inductor 604 can bedetermined from Eq. 1. Assuming that the resonator 102 has an equivalentcapacitance of 20 pF, then the value of the inductor 604 should beapproximately 100 μH (or greater) in order to assure that the parasiticresonance is at 3 MHZ or below. Note that if the additional capacitance224 (FIG. 2E) is utilized for tuning the crystal resonance, then thecapacitance that is used to calculate the inductor 604 is the parallelcombination of C_(ADD) 224 and C_(P) 218.

[0067] The resistor 606 dampens out any unwanted parasitic oscillationsthat are caused by the addition of the inductor 604. The parasiticoscillations correspond to the parasitic resonance that was describedabove for the inductor 604. It is preferable to suppress these parasiticoscillations even if the parasitic oscillation frequency is far removedfrom the intended oscillation frequency because the parasiticoscillations will divert signal power from the intended oscillationfrequency, possibly to the extent of completely suppressing the intendedoscillation. Additionally, the parasitic oscillations will frequency mixwith intended oscillation frequency, and generate spurious signals inthe output oscillator signal 112, which reduces overall spectral purity.

[0068] The value of the resistor 606 should be sufficiently large tosuppress the unwanted oscillations that are associated with the inductor604. However, the resistor 606 should be no larger than necessary as theresistor 606 generates unwanted thermal noise that increases with theresistance value according to Eq. 4. The thermal noise of the resistor606 increases the phase noise of the oscillator output signal 112 justlike the bias resistor 106, and therefore defeats the purpose of thefeedback circuit 602 if the resistor 606 is too large. The exact valueof the resistor 606 will depend on the specific application, circuitconfiguration, and active device gain, as will be understood by thoseskilled in the relevant arts. In embodiments, the value of the resistor606 should be less the value of the bias resistor 106. In embodiments,the resistor 606 is a potentiometer (i.e. variable resistor), whichallows for a variable amount of resistance to be added to or subtractedfrom the feedback circuit 602. In alternate embodiments, the resistor606 is a fixed resistor.

[0069] The flowchart 700 further describes the operation of theoscillator circuit 600, and phase noise reduction according to thepresent invention. The order of the steps in the flowchart 700 is notlimiting as some (or all) of the steps can be performed simultaneouslyor in a different order, as will be understood by those skilled in therelevant arts.

[0070] In step 702, the resonator 102 causes the active device 104 tooscillate at the resonant frequency f₀ of the resonator 102, generatingthe output signal 112 that is preferably a pure tone at f₀. Theresonator 102 provides a positive feedback path for the active device104 at the resonant frequency f₀, thereby causing the active device 104to oscillate at f₀. The resonator 102 can be anyone of the resonatorsthat are shown in FIGS. 2A-2F, or other resonators that will be apparentto those skilled in the relevant arts based the discussion given herein.In a preferred embodiment, the crystal 224 is the resonator of choicebecause of its superior Q as described herein.

[0071] In step 704, the bias resistor 106 generates thermal noise. Themagnitude of the thermal noise voltage increases with temperature,resistance, and circuit bandwidth, according to Eq. 4.

[0072] In step 706, the external inductor circuit 602 shorts out atleast some of the thermal noise that is generated by the bias resistor106, and prevents this thermal noise from increasing the phase noisefloor of the oscillator output signal 112.

[0073] More specifically, the inductor 604 and the resistor 606 providea DC feedback path (and a low frequency feedback path) between theterminals 108 and 110 of the active device 104. The resistor 606 dampensout any parasitic oscillations that are caused by the inductor 604resonating with the capacitance in the resonator 102.

[0074] In step 708, the additional capacitance C_(ADD) 224 can be tunedto adjust the center frequency of the oscillator 600. When the crystal214 is used as the resonator 102, the capacitance 224 is often added inparallel with the crystal 214 to fine tune the oscillator frequency. Ifthe DC feedback circuit 602 causes the oscillator frequency to shift,then the capacitance 224 can be adjusted to compensate for the frequencyshift.

[0075]FIG. 10 illustrates an oscillator circuit 1000 that has analternate configuration for the external inductor circuit. Morespecifically, the oscillator circuit 1000 has an external inductorcircuit 1002 with two resistors 1004 a and 1004 b, in addition to theinductor 604. The resistors 1004 are approximately ½ of the value of theresistor 606 that is shown in FIG. 6.

[0076] 3. Differential Crystal Oscillator and Phase Noise Reduction:

[0077]FIG. 8 illustrates a differential crystal oscillator 800 as oneembodiment of the crystal oscillator 100. The differential crystaloscillator 800 is meant for example purposes only and is not meant tolimit the invention in any way. Other oscillator configurations could beutilized to practice the invention, as will be understood by thoseskilled in the relevant arts based on the discussions given herein.

[0078] The differential crystal oscillator 800 includes a current source802, an active device 804, bias resistors 810 a and 810 b, an activebias circuit 812, and a crystal resonator 214. The active device 804oscillates at the resonant frequency f₀ of the crystal 214, to produce adifferential output signal 821 that can be taken across the nodes 820 aand 820 b. The active bias circuit 812 and the bias resistors 810provide DC bias for the active device 804. The structure and operationof the differential crystal oscillator 800 is discussed in furtherdetail as follows.

[0079] The active device 804 includes cross-coupled transistors 806 aand 806 bthat oscillate at the resonant frequency of the crystal 214.The drain of transistor 806 a is coupled to the gate of transistor 806 bthrough a capacitor 808 a. Likewise, the drain of transistor 806 b iscoupled to the gate of the transistor 806 a through a capacitor 808 b.This cross coupled arrangement provides a feedback path for AC signalsthat pass through the capacitors 808. The crystal 214 is coupled acrossthe nodes 820 a and 820 b, which are also the drains of the respectivetransistors 806 aand 806 b. As such, the crystal 214 is coupled inparallel with feedback path for the cross coupled transistors 806 a and806 b. At resonance, the impedance of the crystal 214 becomes an opencircuit, and causes a positive feedback condition to exist between thetransistors 806 at the resonant frequency f₀ of the crystal 214.

[0080] The positive feedback causes the transistors 806 to oscillate atthe resonant frequency f₀ of the crystal 214, and produce thedifferential output signal 821 that can be taken across the nodes 820 aand 820 b. The capacitors 818 a and 818 b are used to tune to the outputfrequency of the crystal oscillator 800, and therefore function as thecapacitor C_(DD) 224 in FIG. 2F.

[0081] The transistors 806 are not directly coupled to each otherbecause doing so would cause the transistors to latch-up. In otherwords, one transistor 806 would turn-on all the way and the othertransistor 806 would be cutoff, preventing the desired oscillation. Thecapacitors 808 prevent the lock-up condition by blocking DC feedbackbetween the respective gates and drains of the transistors 806.

[0082] The active bias circuit 812 includes two diode connectedtransistors 816 aand 816 b. The resistor 814 a connects the drain andgate of the transistor 816 a to form the diode connection for thetransistor 816 a. The resistor 814 b connects the drain and gate of thetransistor 816 b to form the diode connection for transistor 816 b. Thediode connected transistors 816 a and 816 b provide a stable common modedrain voltage at nodes 820 a and 820 b, based on the current source 802.

[0083] The bias resistors 810 a and 810 b are also connected to thenodes 820 a and 820 b (through the resistors 814) and provide gate biasvoltage for the transistors 806. More specifically, the resistor 810 aprovides DC bias for the gate of the transistor 806 b, and the resistor810 b provides DC bias for the gate of the transistor 806 a.

[0084] As shown, the bias resistors 810 are also connected to thefeedback capacitors 808, and shunt away some of the feedback signal thatis meant for the transistors 806, thereby reducing the overall gain ofthe transistors 806. If the gain is reduced too much, then the positivefeedback will be quashed, and the transistors 806 will not oscillate asintended. Therefore, the resistors 810 should be relatively large tomaintain the gain of the active circuit 804. In embodiments, the valueof the resistors 810 are in the 10 k ohm range, but other resistorvalues could be utilized as will be understood by those skilled in therelevant arts. The bias resistors 810 generate thermal noise voltagethat increases with their resistance value according to the Eq. 4. Asdiscussed herein, this thermal noise voltage is undesirable because itincreases the phase noise floor of the oscillator output signal.

[0085] The differential crystal oscillator 800 is further described inU.S. Patent Application entitled, “Differential Crystal Oscillator”, SerNo. 09/438,689, filed on Nov. 12, 1999, Attorney docket no.33758/LTR/B6, which is incorporated herein by reference in its entirety.

[0086]FIG. 9 illustrates the oscillator 800 with the inductor circuit602 connected across the output nodes 820 a and 820 b of the oscillator800. The inductor circuit 602 is also in parallel with the crystal 214.The inductor circuit 602 provides a DC feedback path across the outputnodes 820 a and 820 b for any thermal noise from the bias resistors 810and the feedback resistors 814. As such, the thermal noise from the biasresistors 810 and the feedback resistors 814 is shorted-out and doesincrease the phase noise of the oscillator output signal 821.

[0087] As stated above, the inductor circuit 602 is in parallel with thecrystal 214.

[0088] Therefore, the inductor 604 can resonant with the equivalentcapacitance of the crystal 214 to cause an (unwanted) parasiticresonance. For instance, the inductor 604 could resonate with thepackage capacitance 218 (FIG. 2D) or the combination of the packagecapacitance 218 and the added capacitance 224 (FIGS. 2E-F). Preferably,the value of the inductor 604 is sufficiently large so this parasiticresonance does not shift the oscillation frequency of the oscillator 800from the resonant frequency f₀ of the crystal 214. Accordingly, theparallel combination of the inductor 604 and the crystal 214 should notsubstantially shift the resonant frequency f₀ of the crystal 214, so asnot to change the operating frequency of the oscillator 800. This can beaccomplished by assuring that the parasitic resonance caused by theinductor 604 is lower than the intended resonant frequency of thecrystal 214 by at least approximately a factor of {square root}{squareroot over (0.1)}. For example and without limitation, if the crystal 214is resonant at 10 MHZ, then the parasitic resonance caused by theinductor 604 should preferably be approximately 3 MHZ, or less. For agiven capacitance value, a minimum value for the inductor 604 can bedetermined from Eq. 1. For example, if the crystal 214 has an equivalentcapacitance of 20 pF, then the value of the inductor 604 shouldpreferably be approximately 100 μH (or greater) in order to assure thatthis parasitic resonance is at 3 MHZ or below. Note that if the addedcapacitance 224 (FIGS. 2E-F) is utilized for tuning the crystalresonance, then the total capacitance that is used for in thedetermination of the inductor 604 is the parallel combination of thecapacitor 224 and the capacitor 218.

[0089] The resistor 606 dampens out any unwanted parasitic oscillationsthat are caused by the addition of the inductor 604. The parasiticoscillations correspond to the parasitic resonance that was describedabove for the inductor 604. It is important to suppress these unwantedoscillations even if the parasitic oscillation frequency is far removedfrom the intended oscillation frequency because the parasiticoscillations will divert signal power from the intended oscillationfrequency. Additionally, parasitic oscillations will frequency mix withintended oscillation frequency and generate spurious signals in theoutput oscillator signal 821, which reduces overall spectral purity ofthe oscillator signal 821.

[0090] The value of the resistor 606 should be sufficiently large tosuppress the unwanted oscillation modes caused by the inductor 602.However, the resistor 606 should be no larger than necessary as theresistor 606 generates unwanted thermal noise that increases with theresistance value according to Eq. 4. The thermal noise of the resistor606 increases the phase noise of the oscillator output signal 821 justlike the bias resistors 810, and therefore defeats the purpose of theinductor circuit 602 if the resistor 606 is too large. As such, theresistor 606 should be no larger than the bias resistors 810, which areapproximately 10 k ohms for some applications. In embodiments, theresistor 606 is a potentiometer (i.e. variable resistor), which allowsfor a variable amount of resistance to be efficiently added to orsubtracted from the inductor circuit 602.

[0091] 4. External Inductor Determination

[0092] As stated above, in embodiments of the invention, the inductor604 is selected so that the parasitic resonance that is caused by theinductor 604 is approximately {square root}{square root over (0.1)} ofthe frequency of the desired resonance of the crystal 214. The followingdiscussion and equations provide mathematical support for thisdetermination.

[0093] Referring to FIG. 2F, the parallel resonance for the crystal 214occurs at the frequency where the admittance of the series resonantcircuit 217 cancels the admittance of (C_(P) 218 || C_(ADD) 224).Assuming in the equations below that C_(p)=(C_(P) 218 || C_(ADD) 224),then the parallel resonance is determined by the equation 5 below:$\begin{matrix}{\omega_{p} = \sqrt{\omega_{s}^{2} + \frac{1}{C_{p}L_{M}}}} & {{Eq}.\quad 5} \\{\omega_{s} = \frac{1}{\sqrt{L_{M}C_{M}}}} & {{Eq}.\quad 6}\end{matrix}$

[0094] where

[0095] When the external inductor circuit 602 is included as in FIG. 6,and ignoring the series resistor 606, then it can be shown that theparallel resonance becomes: $\begin{matrix}{\omega_{p} \approx {\omega_{s} + {\frac{1}{2}\frac{C_{M}}{C_{p}\left( {1 - \frac{\omega_{parasitic}^{2}}{\omega_{p}^{2}}} \right)}}}} & {{Eq}.\quad 7}\end{matrix}$

[0096] where ω_(parasitic) represents the (unwanted) low frequencyresonance that is caused by the external inductor 604 resonating withC_(p). Based on Eq. 7 it is desirable that: $\begin{matrix}{\frac{\omega_{parasitic}^{2}}{\omega_{p}^{2}} \leq 0.1} & {{Eq}.\quad 8}\end{matrix}$

[0097] According to Equation 8, it is preferable that the frequency ofthe parasitic resonance is approximately {square root}{square root over(0.1)} of the frequency of the desired resonance, or lower. Statedanother way, the parasitic resonance is preferably lower than thefrequency of the desired resonance by at least approximately a factor of{square root}{square root over (10)}. The result is that the effect ofthe external inductor 604 on the parallel resonance of the crystal 214will be less than the tolerance of the additional capacitor 224, whichis typically 5-10% of the capacitor 224 value.

[0098] 5. Other Applications

[0099] The noise reduction invention described herein has been discussedin reference to a crystal oscillator. However, the noise reductioninvention is not limited to crystal oscillators. The noise reductioninvention is applicable to other oscillator circuit configurations,including oscillator circuits that use other types of resonators, suchas discrete circuit elements. Additionally, the noise reductioninvention is applicable to other (non-oscillator) active circuits thatcan benefit from a low frequency feedback path that shorts-out thermalnoise. The application of this noise reduction invention to these otheractive circuits will be understood by those skilled in the relevant artsbased on the discussions given herein, and are within the scope andspirit of the present invention.

[0100] 6. Conclusion

[0101] Example embodiments of the methods, systems, and components ofthe present invention have been described herein. As noted elsewhere,these example embodiments have been described for illustrative purposesonly, and are not limiting. Other embodiments are possible and arecovered by the invention. Such other embodiments will be apparent topersons skilled in the relevant art(s) based on the teachings containedherein. Thus, the breadth and scope of the present invention should notbe limited by any of the above-described exemplary embodiments, butshould be defined only in accordance with the following claims and theirequivalents.

What is claimed is:
 1. An oscillator circuit, comprising: a resonatorhaving a resonant frequency; an active device, coupled to saidresonator, said active device capable of oscillating at said resonantfrequency of said resonator; and an inductor circuit connected to saidactive device and in parallel with said resonator, whereby said inductorcircuit shorts-out thermal noise associated with said active device. 2.The oscillator circuit of claim 1, wherein said inductor circuit isconnected across output terminals of the active device.
 3. Theoscillator circuit of claim 2, wherein said inductor circuit provides aDC feedback path between said output terminals.
 4. The oscillatorcircuit of claim 1, wherein said inductor circuit includes an inductorthat is connected in series with a resistor.
 5. The oscillator circuitof claim 4, wherein a value of said inductor is such that said inductordoes not shift said resonant frequency of said resonator.
 6. Theoscillator circuit of claim 4, wherein a value of said inductor is suchthat a parallel combination of said inductor and said resonator has aresonant frequency that is substantially the same as that of saidresonator.
 7. The oscillator circuit of claim 4, wherein a value of saidinductor is such that any parasitic resonance that is caused by saidinductor is lower in frequency than said resonant frequency of saidresonator by a factor of at least {square root}{square root over (0.1)}.8. The oscillator circuit of claim 7, wherein said resistor quashes atleast one parasitic oscillation that is associated with said inductor.9. The oscillator circuit of claim 1, wherein said resonator is acrystal resonator.
 10. The oscillator circuit of claim 9, furthercomprising an additional capacitor that is connected in parallel withsaid crystal resonator.
 11. The oscillator circuit of claim 10, whereinsaid additional capacitor compensates for any frequency shift caused bysaid inductor circuit.
 12. The oscillator circuit of claim 1, whereinsaid resonator is a series inductor-capacitor resonant circuit.
 13. Theoscillator circuit of claim 1, wherein said resonator is a parallelinductor-capacitor resonant circuit.
 14. The oscillator circuit of claim1, further comprising at least one bias resistor that is associated withsaid oscillator circuit.
 15. The oscillator circuit of claim 14, whereinsaid inductor circuit shorts-out thermal noise generated by said biasresistor.
 16. The oscillator circuit of claim 14, wherein said resistorin said inductor circuit is less than said bias resistor.
 17. Theoscillator circuit of claim 1 ,-wherein said active device includes across-coupled pair of transistors.
 18. The oscillator circuit of claim17, wherein said cross-coupled pair of transistors are AC coupled. 19.The oscillator circuit of claim 17, further comprising: an active biascircuit to bias said cross-coupled pair of transistors; and at least onebias resistor that connects said bias circuit to said cross-coupled pairof transistor.
 20. The oscillator circuit of claim 19, wherein saidinductor circuit shorts-out thermal noise that is generated by said atleast one bias resistor.
 21. A method of generating a periodic signalhaving low phase noise, the method comprising the steps of: (1) biasingan active device using at least one resistor; (2) causing said activedevice to oscillate at a resonant frequency, thereby producing theperiodic signal; and (3) shorting-out thermal noise that is generated bysaid at least one resistor, thereby reducing the effect of said thermalnoise on the phase noise of the periodic signal.
 22. The method of claim21, wherein said periodic signal is produced at output terminals of saidactive device, and wherein step (3) comprises the step of providing a DCfeedback path across said output terminals of said active device. 23.The method of claim 22, further comprising the step of: (4) suppressingat least one parasitic oscillation that is associated with said DCfeedback path.
 24. The method of claim 21, further comprising the stepof: (4) tuning a frequency of the periodic signal to compensate for anyfrequency shift caused by said DC feedback path.
 25. The method of claim24, wherein step (4) comprises the step of tuning a capacitance coupledto said active device.
 26. The method of claim 21, wherein step (2)comprises the step of providing a positive feedback path for said activedevice.
 27. An oscillator circuit, comprising: a resonator having aresonant frequency; an active device coupled to said resonator, saidactive device capable of oscillating at said resonant frequency; atleast one bias resistor to bias said active device; and means forreducing the effect of thermal noise associated with said bias resistoron a phase noise floor of said oscillator circuit.
 28. The oscillatorcircuit of claim 27, wherein said means for reducing comprises means forshorting-out thermal noise that is associated with said at least onebias resistor.
 29. The oscillator circuit of claim 27, wherein saidmeans for reducing comprises an inductor circuit coupled to said activedevice, said inductor circuit including an inductor and a resistor thatare connected in-series.
 30. The oscillator circuit of claim 27, whereinsaid inductor is large enough that a parasitic resonance caused by saidinductor is lower in frequency than said resonant frequency of saidresonator by at least a factor of {square root}{square root over (0.1)}.31. The oscillator circuit of claim 30, wherein said resistor in saidinductor circuit is large enough to prevent said active device fromoscillating at said parasitic resonance.
 32. The oscillator circuit ofclaim 31, wherein said resistor in said inductor circuit is not largerthan said at least one bias resistor.
 33. An oscillator circuit,comprising: a crystal resonator having a resonant frequency; an activedevice, coupled to said resonator, said active device capable ofoscillating at said resonant frequency; at least one bias resistor tobias said active device; and an inductor circuit coupled across outputterminals of said active device, said inductor circuit including aninductor and a resistor that are connected in series.
 34. The oscillatorcircuit of claim 33, wherein said crystal resonator is connected to saidoutput terminals of said active device, and in-parallel with saidinductor circuit.
 35. The oscillator circuit of claim 33, wherein saidinductor circuit provides a DC feedback path between said oscillatoroutput terminals so as to short-out thermal noise from said at least onebias resistor.
 36. The oscillator circuit of claim 33, wherein saidinductor in said inductor circuit is large enough that a parasiticresonance caused by said inductor is lower in frequency than saidresonance of said resonator by at least a factor of {square root}{squareroot over (0.1)}.
 37. The oscillator circuit of claim 36, wherein saidresistor in said inductor circuit is large enough to prevent said activedevice from oscillating at said parasitic resonance.
 38. The oscillatorcircuit of claim 37, wherein said resistor value is smaller than a valueof said at least one bias resistor.
 39. The oscillator circuit of claim33, wherein said active device includes a pair of cross-coupledtransistors that are AC coupled.
 40. The oscillator circuit of claim 39,wherein said crystal resonator causes a positive feedback path for saidcross-coupled transistors at said resonant frequency, thereby causingsaid cross-coupled transistors to oscillate.